# How to Play Lotto Max

In Canada, Lotto Max is a national lottery played in all 13 provinces and territories. Each ticket costs \$5.00 and includes three selections. The purchaser may pick the first set of numbers and let the computer pick the other two sets, or the let the computer make all three selections. The object is to match 7 distinct numbers between 1 and 49.

An eighth bonus number is also selected for each drawing; this number only comes into play when you match exactly 6 out of 7 or 3 out of 7 regular numbers. (It is not possible to match 7 out of 7 + the bonus because you can only select 7 numbers, and there are no special prizes for selecting 5 out of 7 + bonus, or 4 out of 7 + bonus.)

In Lotto Max, the Jackpot is capped at 50 million dollars. Any jackpot amount in excess of 50 million is parceled out in bonus max millions drawings, in which the lottery officials draw new sets of 7 numbers worth \$1,000,000 each.

### Lotto Max Odds

For a \$5.00 ticket containing 3 selections, the odds of obtaining winning matches are as follows:

7 out of 7:
3*1/(49 c 7) = 3*(7*6*5*4*3*2*1)/
/(49*48*47*46*45*44*43) = 1/28633528
PRIZE: 87% of pool

6 out of 7 + bonus:
3*[(7 c 6)(41 c 0)]/[49 c 7] = 1/4090504
PRIZE: 4% of pool

6 out of 7, no bonus:
3*[(7 c 6)(41 c 1)]/[49 c 7] = 41/4090504 ≈ 1/99768
PRIZE: 4% of pool

5 out of 7:
3*[(7 c 5)(42 c 2)]/[49 c 7] = 18081/28633528 ≈ 1/1584
PRIZE: 5% of pool

4 out of 7:
3*[(7 c 4)(42 c 3)]/[49 c 7] = 401800/28633528 ≈ 1/71
PRIZE: \$20

3 out of 7 + bonus:
3*[(7 c 3)(41 c 3)]/[49 c 7] = 373100/28633528 ≈ 1/77
PRIZE: \$20

3 out of 7, no bonus
3*[(7 c 3)(41 c 4)]/[49 c 7] = 3544450/28633528 ≈ 1/8
PRIZE: free Lotto Max ticket (\$5 value)

There are no prizes for matching less than 3 numbers out of 7. The total odds of winning any prize are

(1 + 7 + 41 + 18081 + 401800 + 373100 + 3544450)/28633528
≈ 3/20 or 15%

All prizes are split evenly among the number of winning tickets. For example, matching 6 out of 7 with no bonus earns 4% of the pool funds. If 16 people win this prize level, then each person gets (4/16) = 0.25% of the pool funds.